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Mathematics Math Shortcuts Math Shortcut to Tell if a Number is Divisible by 6 (Rule #3)
Mathematics Math Shortcuts Math Shortcut to Tell if a Number is Divisible by 6 (Rule #3)
Written by Andrew B. Bartels, October 2011
Rule #3 for Division by 6, high magnitude method (see also Rule #1 or Rule #2 for alternate methods):
A number is evenly divisible by 6 if the sum of the right digit + the sum of the (remaining digits X 4) is evenly divisible by 6.
Example 1:
Number: 4,353,564,678
1. Compute the sum of each of the digits multiplied by 4, except for the least significant digit, which is simply added to the total:
| 4 x 4 = | 16 |
| 3 x 4 = | 12 |
| 5 x 4 = | 20 |
| 3 x 4 = | 12 |
| 5 x 4 = | 20 |
| 6 x 4 = | 24 |
| 4 x 4 = | 16 |
| 6 x 4 = | 24 |
| 7 x 4 = | 28 |
| 8 => | 8 |
| Sum = | 180 |
2. The sum of 180 is evenly divisibly by 6 (the answer is 30), therefore 4,353,564,678 is evenly divisible by 6 (the answer is 725,594,113)
Note: The remainder if the sum divided by 6 is also the remainder of the larger number divided by 6.
